In the production of gears, especially bevel gears, two types of processes are commonly employed, generating processes and non-generating processes.
Generating processes can be divided into two categories, face milling (intermittent indexing) and face hobbing (continuous indexing). In generating face milling processes, a rotating tool is fed into the workpiece to a predetermined depth. Once this depth is reached, the tool and workpiece are then rolled together in a predetermined relative rolling motion, known as the generating roll, as though the workpiece were rotating in mesh with a theoretical generating gear, the teeth of the theoretical generating gear being represented by the stock removing surfaces of the tool. The profile shape of the tooth is formed by relative motion of the tool and workpiece during the generating roll.
In generating face hobbing processes, the tool and workpiece rotate in a timed relationship and the tool is fed to depth thereby forming all tooth slots in a single plunge of the tool. After full depth is reached, the generating roll is commenced.
Non-generating processes, either intermittent indexing or continuous indexing, are those in which the profile shape of a tooth on a workpiece is produced directly from the profile shape on the tool. The tool is fed into the workpiece and the profile shape on the tool is imparted to the workpiece. While no generating roll is employed, the concept of a theoretical generating gear in the form of a theoretical “crown gear” is applicable in non-generating processes. The crown gear is that theoretical gear whose tooth surfaces are complementary with the tooth surfaces of the workpiece in non-generating processes. Therefore, the cutting blades on the tool represent the teeth of the theoretical crown gear when forming the tooth surfaces on the non-generated workpiece.
On machines for manufacturing gears, one or more compensations may be performed in order to eliminate tooth spacing deviations. Spacing deviations can be caused by tool wear, temperature change of tool, work and machine components. Those causes influence the relationship between tool and work whereby they are grouped in three categories (applies to face milling only, i.e. intermittent indexing):                Rapid Effect—only the first few slots (e.g. the first three slots) of the total number of slots on a gear (e.g. 35 slots) are influenced;        Medium term effect—during one revolution of a gear, the slots from the first to the last slot will be influenced; and        Long term effect—the slot spacing characteristics of workpieces, in the course of a manufacturing shift, will be influenced.        
Since workpieces are connected, via workholding equipment, to a machine work spindle in a non-rotational oriented way, spindle runout and runout between workholding and machine spindle have a random relationship to the spacing errors mentioned before. This is because the rotational stop position of work spindles in gear manufacturing machines is generally random. If the first slot of a bevel ring gear slot is cut on a cutting machine in the 9 o'clock position, then any spacing compensation bases on the absolute spindle orientation in that position. Commonly, the absolute work spindle rotational angle will be different from part to part. A compensation which addresses the rapid, medium and/or long term effect of spacing variation will not influence the component resulting from spindle or workholding runout. On the contrary, spindle or workholding runouts will adversely affect the result of a spacing error compensation.
Runout may be defined as a deviation from a desired form or orientation of a part's surface when rotated through 1 revolution (360 degrees). Two types of runout are commonly referred to: (1) radial runout, which is the deviation in a direction perpendicular to the axis of rotation of a body such as a workpiece or tool, and (2) axial runout, which is the amount along the axis of rotation by which the rotation of a body, such as a workpiece or tool, deviates from a plane.
If the machine work spindle is always oriented in the same rotational position at the beginning of the machining process for each part, then a measurement of the machined gear could capture some portion of the radial and axial run-out. However, in dry cutting for example, this would be compensated such as by a first-order ramp function from the first to the last tooth (based on the assumption that the medium term effect is caused by a work temperature increase from slot to slot and the fact that the last slot, which has the highest temperature, is adjacent to the first slot which had time to cool down during the time the remaining slots (e.g. 34) were cut). Such a compound correction of a mix of temperature effect as well as spindle and workholding runout can only be partially successful, and in most cases does not result in significant tooth spacing error reductions.
In gear grinding, spacing error compensation addresses, commonly, the rapid effect and the medium term effect in two ramps (superimposed to the axial and radial work position). This compensation minimizes the influence of grinding wheel wear between two dressings. A machine temperature compensation is generally done independently and addresses relevant machine axes depending on the individual machine design. The wheel wear compensation as described is not suited to compensate for workholding and spindle runout.
In the case of a non-oriented spindle and workholding arrangement, it has to be considered that every time the workholding fixture is removed and mounted back on the work spindle, the orientation between workholding fixture and spindle is different which will cause a phase shift in rotational orientation between spindle and workholding which will interfere with the attempt to apply the spacing error compensation that was developed previously for the subject job.
In the case of an oriented spindle having an oriented (keyed) positioning of the workholding fixture to the machine work spindle, it has to be considered that the seating of the workholding in the taper of the machine work spindle is different every time it is removed and remounted. This difference even increases in case of an oriented (keyed) position of the workholding. Small differences of only several microns will adversely affect the tooth spacing result. Some tooth spacing error compensations use single or multiple ramp functions or are developed for every slot individually.
Workholding runout delivers a sinusoidal tooth spacing error from the first to the last slot (radial runout) or a sinusoidal slot depth variation from the first to the last slot (axial runout).
After mounting a workholding fixture to a gear manufacturing machine, the runout (mostly radially) is measured with an indicator. In many cases, the workholding is rotated about 90° or 180° to find a more optimal relative angle to the work spindle in order to cancel out some or the entire runout. None of today's spacing error compensation methods are suited to capture the two types of runout, neither are they suited to reduce or eliminate them.